To Fridge Or Not To Fridge?

I am making a fondant cake with the chunky strawberry filling in the recipe area. The recipe is below. My question is does this need to be put in the fridge? It's being picked up on Thursday night for the next day. I am just worried about the fondant being sticky if it's in the fridge. AHHHH.....what do I do???

Unthaw frozen strawberries and keep liquid. Place strawberries with liquid in saucepan and using kitchen scissors cut into small chunks. Mix sugar and corn starch together. Add mixture to chunky strawberries and mix together. Heat until bubbling-stirring constantly. Boil about two minutes. Cool and fill cake.